Quasicontinuous Functions with Everywhere Discontinuous Iterates



Real Analysis Exchange

Quasicontinuous Functions with Everywhere Discontinuous Iterates

M. Sohaib Alam and Annalisa Crannell

Source: Real Anal. Exchange Volume 33, Number 1 (2007), 161-166.

Abstract

This paper gives examples of two \qcont{} functions whose second iterates are discontinuous everywhere. It is well-known that every \qcont function has a dense---indeed, residual---set of points of continuity; our counter-examples show that this property does not hold for compositions of such functions.

Primary Subjects: 54C08, 54H20
Keywords: iteration; quasicontinuity; quasicontinuous function

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.rae/1209398386
Mathematical Reviews number (MathSciNet): MR2402871


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